The interesting thing (to me, at the moment) about Fat Man Down is that the two sets of players have different rules and the rules deceive each group. Perhaps that is how to tie the game into the theme. You can only play once (or only play as the astronaut once) because you discover that the natives have their own rules to play by.

Another weird idea I (probably) won't follow up on: the game is some sort of parable. The astronaut is God or an angel, come down to help the native culture, but they cannot understand him/her. But how does an angel reveal their divine message if they can't speak the language? You can only play once, because once the secret is revealed or discovered, the scenario is busted.